The broad objective of the proposed research is to develop new methods of determining the structural and dynamic implications of nuclear magnetic resonance (NMR) data on proteins and other biological macromolecules in solution. Such detailed knowledge of both structure and dynamics is needed in order to understand the function of biological macromolecules in terms of the basic principles of physics and chemistry, and hence plays a vital role in the solution of many important problems in biology and medicine. Within the scope of this broad objective we distinguish the following specific aims: (1) To study the sensitivity to measurement errors of the molecular conformations obtained by fitting them to "NOESY" cross-peak intensities or spectra; this will be done by applying such structure determination and refinement methods to simulated test problems. (2) To further develop methods of assigning relative concentrations to ensembles of conformations so that the weighted average NMR parameters best-fit those derived from the spectra; the sensitivity of these methods to errors will also be evaluated. (3) To further develop methods of deriving as many proton-proton coupling constants from "COSY-type" spectra as precisely as possible, since such measurements promise to greatly alleviate the sensitivity problems in specific aims (1) and (2); this will be done by fitting simulated spectra to observed spectra. (4) To develop new methods of extracting cross-relaxation rates from NOESY spectra more completely and precisely than is currently possible, since these measurements should likewise improve the precision and reliability of the results obtained in (1) and (2); this will be done by a combination of simulation and inversion techniques. (5) To develop novel methods of assigning reliable error bounds to measurements of relaxation rates, which can be converted directly to distance bounds for structure determination; this will require basic research into the mathematical relations between the rates, cross-peak intensities and spectra. (6) To apply the methods developed in (1) through (5) above to ongoing studies of biomolecular structure and dynamics, particularly heteronuclear relaxation.